
/* @(#)e_log10.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#include "math.h"
#include "float.h"
#include "k_log.h"

static const double
two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
ivln10hi   =  4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
ivln10lo   =  2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */

static const double zero   =  0.0;
static volatile double vzero = 0.0;

double
__ieee754_log10(double x)
{
    double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2;
    int i,k,hx;
    unsigned int lx;

    EXTRACT_WORDS(hx,lx,x);

    k=0;
    if (hx < 0x00100000) {            /* x < 2**-1022  */
        if (((hx&0x7fffffff)|lx)==0)
        return -two54/vzero;        /* log(+-0)=-inf */
        if (hx<0) return (x-x)/zero;    /* log(-#) = NaN */ /*lint !e414*/
        k -= 54; x *= two54; /* subnormal number, scale up x */
        GET_HIGH_WORD(hx,x);
    }
    if (hx >= 0x7ff00000) return x+x;
    if (hx == 0x3ff00000 && lx == 0)
        return zero;            /* log(1) = +0 */
    k += (hx>>20)-1023;
    hx &= 0x000fffff;
    i = (hx+0x95f64)&0x100000;
    SET_HIGH_WORD(x,hx|(i^0x3ff00000));    /* normalize x or x/2 */
    k += (i>>20);
    y = (double)k;
    f = x - 1.0;
    hfsq = 0.5*f*f;
    r = k_log1p(f);

    /* See e_log2.c for most details. */
    hi = f - hfsq;
    SET_LOW_WORD(hi,0);
    lo = (f - hi) - hfsq + r;
    val_hi = hi*ivln10hi;
    y2 = y*log10_2hi;
    val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;

    /*
     * Extra precision in for adding y*log10_2hi is not strictly needed
     * since there is no very large cancellation near x = sqrt(2) or
     * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
     * with some parallelism and it reduces the error for many args.
     */
    w = y2 + val_hi;
    val_lo += (y2 - w) + val_hi;
    val_hi = w;

    return val_lo + val_hi;
}

double log10(double x)
{
  return __ieee754_log10(x);
}